LAB 4G: Growing Trees
Lab 4G  Growing trees
Directions: Follow along with the slides, completing the questions in blue on your computer, and answering the questions in red in your journal.
Trees vs. Lines

So far in the labs, we've learned how we can fit linear models to our data and use them to make predictions.

In this lab, we'll learn how to make predictions by growing trees.
– Instead of creating a line, we split our data into branches based on a series of yes or no questions.
– The branches help sort our data into leaves which can then be used to make predictions.

Start, by loading the
titanic
data.
Our first tree

Use the
tree()
function to create a classification tree that predicts whether a personsurvived
the Titanic based on theirgender
.– A classification tree tries to predict which category a categorical variable would belong to based on other variables.
– The syntax for
tree
is similar to that of thelm()
function.– Assign this model the name
tree1
. 
Why can't we just use a linear model to predict whether a passenger on the Titanic
survived
or not based on theirgender
?
Viewing trees

To actually look at and interpret our
tree1
, place the model into thetreeplot
function.– Write down the labels of the two branches.
– Write down the labels of the two leaves.

Answer the following, based on the
treeplot
:– Which
gender
does the model predict will survive?– Where does the plot tell you the number of people that get sorted into each leaf? How do you know?
– Where does the plot tell you the number of people that have been sorted incorrectly in each leaf?
Leafier trees

Similar to how you included multiple variables for a linear model, create a
tree
that predicts whether a personsurvived
based on theirgender
,age
,class
, and where theyembarked
.– Call this model
tree2
. 
Create a treeplot for this model and answer the following question:
– Mrs. Cumings was a 38yearold female with a 1st class ticket from Cherbourg. Does the model predict that she survived?
– Which variable ended up not being used by
tree
?
Tree complexity

By default, the
tree()
function will fit a tree model that will make good predictions without needing lots of branches. 
We can increase the complexity of our trees by changing the complexity parameter,
cp
, which equals0.01
by default. 
We can also change the minimum number of observations needed in a leaf before we split it into a new branch using
minsplit
, which equals20
by default. 
Using the same variables that you used in
tree2
, create a model namedtree3
but includecp = 0.005
andminsplit = 10
as arguments.– How is
tree3
different fromtree2
?
Predictions and Crossvalidation

Just like with linear models, we can use crossvalidation to measure how well our classification trees perform on unseen data.

First, we need to compute the predictions that our model makes on test data.
– Use the
data
function to load thetitanic_test
data.– Fill in the blanks below to predict whether people in the
titanic_test
data survived or not usingtree1
.
Note: the argument
type = "class"
tells thepredict
function that we are classifying a categorical variable instead of predicting a numerical variable.titanic_test < mutate(_, prediction = predict(_, newdata = ____, type = "class"))

Measuring model performance

Similar to how we use the mean squared error to describe how well our model predicts numerical variables, we use the misclassification rate to describe how well our model predicts categorical variables.
– The misclassification rate (MCR) is the number of people who were predicted to be in one category but were actually in another.

Run the following command to see a sidebyside comparison of the actual outcome and the predicted outcome:
View(select(titanic_test, survived, prediction))

Where does the first misclassification occur?
Misclassification rate

In order to tally up the total number of misclassifications, we need to create a function that compares the actual outcome with the predicted outcome. The not equal to operator (!=) will be useful here.

Fill in the blanks to create a function to calculate the MCR.

Hint: sum(_!=_) will count the number of times that the lefthand side does not equal the righthand side.

We want to count the number of times that actual does not equal predicted and then divide by the total number of observations.
calc_mcr < function(actual, predicted) { sum(_ != _) / length(____) }


Then run the following to calculate the MCR.
summarize(titanic_test, mcr = calc_mcr(survived, prediction))
On your own

In your own words, explain what the misclassification rate is.

Which model (
tree1
,tree2
ortree3
) had the lowest misclassification rate for thetitanic_test
data? 
Create a 4th model using the same variables used in
tree2
. This time though, change the complexity parameter to0.0001
. Then answer the following.– Does creating a more complex classification tree always lead to better predictions? Why not?

A regression tree is a tree model that predicts a numerical variable. Create a regression tree model to predict the Titanic's passenger's ages and calculate the MSE.
– Plots of regression trees are often too complex to plot.